Decentralized sliding mode control and estimation for large-scale systems

This thesis concerns the development of an approach of decentralised robust control and estimation for large scale systems (LSSs) using robust sliding mode control (SMC) and sliding mode observers (SMO) theory based on a linear matrix inequality (LMI) approach. A complete theory of decentralized first order sliding mode theory is developed. The main developments proposed in this thesis are: The novel development of an LMI approach to decentralized state feedback SMC. The proposed strategy has good ability in combination with other robust methods to fulfill specific performance and robustness requirements. The development of output based SMC for large scale systems (LSSs). Three types of novel decentralized output feedback SMC methods have been developed using LMI design tools. In contrast to more conventional approaches to SMC design the use of some complicated transformations have been obviated. A decentralized approach to SMO theory has been developed focused on the Walcott-Żak SMO combined with LMI tools. A derivation for bounds applicable to the estimation error for decentralized systems has been given that involves unknown subsystem interactions and modeling uncertainty. Strategies for both actuator and sensor fault estimation using decentralized SMO are discussed.The thesis also provides a case study of the SMC and SMO concepts applied to a non-linear annealing furnace system modelderived from a distributed parameter (partial differential equation) thermal system. The study commences with a lumped system decentralised representation of the furnace derived from the partial differential equations. The SMO and SMC methods derived in the thesis are applied to this lumped parameter furnace model. Results are given demonstrating the validity of the methods proposed and showing a good potential for a valuable practical implementation of fault tolerant control based on furnace temperature sensor faults

Verteilte Zustandsschätzung nichtlinearer Systeme

This thesis presents the combination of the Unscented Kalman Filter with decentralisation, distribution, and fusion techniques. First, the basics of optimal linear state estimation are presented. Besides a focus on practical implications, the non-linear Unscented Kalman Filter is derived. It serves many advantages over other non-linear extensions of the basic algorithm. The similarities of both are shown. Next, decentralisation and distribution techniques for the linear filter are presented and due to the common structure adapted to the unscented filter. Thus, the Distributed And Decentralised Unscented Kalman Filter is derived. To successfully implement those filters the distribution of the global system dynamics is essential. The presented method consists of a partitioning of this global model. Direct states are described by their differential equations. Added states get no dynamics. The observability of non-linear filters and their application to decentralised and distributed cases is discussed. The empirical Gramian observability matrices pose the best possibilities for practical usage. The application of these methodologies is shown for two systems with various conditions. A system of three coupled tanks is used for distributed application. A system of multiple laser trackers is used for both decentralised and distributed application. In its decentralised form the filter yields identical estimation in all nodes. The decentralised form imposes an order reduction of the local systems. Thus, the global state vector is never estimated completely. Besides those applications both a complete loss of one sensor unit and a reconfiguration of the filter network are simulated. The network inherently imposes a robustness against disturbances. Online adaptations of the network topology are possible, as well. The reduction of system orders lead to a reduced need of computational time per node.Die Arbeit handelt von der Kombination des Unscented Kalman-Filters mit den Methoden der Dezentralisierung, Verteilung und Fusion. Zu Anfang werden die allgemeinen Grundlagen der optimalen Zustandsschätzung für das lineare Filter hergeleitet. Aus diesen Betrachtungen, die auch mit Blick auf die praktische Umsetzbarkeit geführt werden, wird dann das Unscented Kalman-Filter beschrieben, welches gegenüber anderen nichtlinearen Erweiterungen deutliche Vorteile bietet. Die Gemeinsamkeiten beider Filterstrukturen werden herausgearbeitet. In der Folge werden zunächst die Dezentralisierung und Verteilung des linearen Filters präsentiert. Auf Grund der Ähnlichkeiten der beiden Filter können diese dann erfolgreich übertragen werden, so dass das Verteilte Und Dezentrale Unscented Kalman-Filter präsentiert werden kann. Zum erfolgreichen Einsatz dieser Methoden ist eine Verteilung eines globalen, nichtlinearen Systemmodells notwendig. Das vorgestellte Verfahren beruht auf einer Partitionierung des Systems. Für direkte Zustände werden die Differentialgleichungen formuliert. Für weitere Zustände wird eine Modellierung ohne eigene Dynamik vorgenommen. Der Frage der Beobachtbarkeit für nichtlineare Filter und deren dezentrale und verteilte Anwendung wird ebenfalls nachgegangen. Es wird gezeigt, dass die Benutzung der empirischen Gramschen Beobachtbarkeitsmatrix für den praktischen Einsatz besonders gut geeignet ist. Die Anwendung dieser Konzepte erfolgt auf zwei Systemen mit unterschiedlichen Voraussetzungen. An einem Dreitanksystem wird das verteilte Filter gezeigt. Danach folgt der Einsatz in einem Multilasertrackersystem. Dieses wird sowohl dezentral als auch verteilt benutzt. Der dezentrale Einsatz des Filters zeigt, dass in allen Filterknoten die Schätzungen miteinander übereinstimmen. Bei der verteilten Schätzung wird durch die damit verbundene Ordnungsreduktion erreicht, dass in den einzelnen Knoten nie der gesamte globale Zustandsvektor geschätzt werden muss. Neben diesen Ansätzen werden auch der Ausfall von Messeinrichtungen und die Umkonfiguration des Systems simuliert. Durch das Filternetzwerk entsteht ein gegenüber Störungen robuster Beobachter. Ebenso können zur Laufzeit Anpassungen der Topologie vorgenommen werden. Die durch die Verteilung entstehende Ordnungsreduktion schlägt sich in einem verringerten Rechenbedarf pro Knoten nieder

Optimal Statistical Rates for Decentralised Non-Parametric Regression with Linear Speed-Up

We analyse the learning performance of Distributed Gradient Descent in the context of multi-agent decentralised non-parametric regression with the square loss function when i.i.d. samples are assigned to agents. We show that if agents hold sufficiently many samples with respect to the network size, then Distributed Gradient Descent achieves optimal statistical rates with a number of iterations that scales, up to a threshold, with the inverse of the spectral gap of the gossip matrix divided by the number of samples owned by each agent raised to a problem-dependent power. The presence of the threshold comes from statistics. It encodes the existence of a "big data" regime where the number of required iterations does not depend on the network topology. In this regime, Distributed Gradient Descent achieves optimal statistical rates with the same order of iterations as gradient descent run with all the samples in the network. Provided the communication delay is sufficiently small, the distributed protocol yields a linear speed-up in runtime compared to the single-machine protocol. This is in contrast to decentralised optimisation algorithms that do not exploit statistics and only yield a linear speed-up in graphs where the spectral gap is bounded away from zero. Our results exploit the statistical concentration of quantities held by agents and shed new light on the interplay between statistics and communication in decentralised methods. Bounds are given in the standard non-parametric setting with source/capacity assumptions

Distributed adaptive signal processing for frequency estimation

It is widely recognised that future smart grids will heavily rely upon intelligent communication and signal processing as enabling technologies for their operation. Traditional tools for power system analysis, which have been built from a circuit theory perspective, are a good match for balanced system conditions. However, the unprecedented changes that are imposed by smart grid requirements, are pushing the limits of these old paradigms. To this end, we provide new signal processing perspectives to address some fundamental operations in power systems such as frequency estimation, regulation and fault detection. Firstly, motivated by our finding that any excursion from nominal power system conditions results in a degree of non-circularity in the measured variables, we cast the frequency estimation problem into a distributed estimation framework for noncircular complex random variables. Next, we derive the required next generation widely linear, frequency estimators which incorporate the so-called augmented data statistics and cater for the noncircularity and a widely linear nature of system functions. Uniquely, we also show that by virtue of augmented complex statistics, it is possible to treat frequency tracking and fault detection in a unified way. To address the ever shortening time-scales in future frequency regulation tasks, the developed distributed widely linear frequency estimators are equipped with the ability to compensate for the fewer available temporal voltage data by exploiting spatial diversity in wide area measurements. This contribution is further supported by new physically meaningful theoretical results on the statistical behavior of distributed adaptive filters. Our approach avoids the current restrictive assumptions routinely employed to simplify the analysis by making use of the collaborative learning strategies of distributed agents. The efficacy of the proposed distributed frequency estimators over standard strictly linear and stand-alone algorithms is illustrated in case studies over synthetic and real-world three-phase measurements. An overarching theme in this thesis is the elucidation of underlying commonalities between different methodologies employed in classical power engineering and signal processing. By revisiting fundamental power system ideas within the framework of augmented complex statistics, we provide a physically meaningful signal processing perspective of three-phase transforms and reveal their intimate connections with spatial discrete Fourier transform (DFT), optimal dimensionality reduction and frequency demodulation techniques. Moreover, under the widely linear framework, we also show that the two most widely used frequency estimators in the power grid are in fact special cases of frequency demodulation techniques. Finally, revisiting classic estimation problems in power engineering through the lens of non-circular complex estimation has made it possible to develop a new self-stabilising adaptive three-phase transformation which enables algorithms designed for balanced operating conditions to be straightforwardly implemented in a variety of real-world unbalanced operating conditions. This thesis therefore aims to help bridge the gap between signal processing and power communities by providing power system designers with advanced estimation algorithms and modern physically meaningful interpretations of key power engineering paradigms in order to match the dynamic and decentralised nature of the smart grid.Open Acces

Catching Cheats: Detecting Strategic Manipulation in Distributed Optimisation of Electric Vehicle Aggregators

Given the rapid rise of electric vehicles (EVs) worldwide, and the ambitious targets set for the near future, the management of large EV fleets must be seen as a priority. Specifically, we study a scenario where EV charging is managed through self-interested EV aggregators who compete in the day-ahead market in order to purchase the electricity needed to meet their clients' requirements. With the aim of reducing electricity costs and lowering the impact on electricity markets, a centralised bidding coordination framework has been proposed in the literature employing a coordinator. In order to improve privacy and limit the need for the coordinator, we propose a reformulation of the coordination framework as a decentralised algorithm, employing the Alternating Direction Method of Multipliers (ADMM). However, given the self-interested nature of the aggregators, they can deviate from the algorithm in order to reduce their energy costs. Hence, we study the strategic manipulation of the ADMM algorithm and, in doing so, describe and analyse different possible attack vectors and propose a mathematical framework to quantify and detect manipulation. Importantly, this detection framework is not limited the considered EV scenario and can be applied to general ADMM algorithms. Finally, we test the proposed decentralised coordination and manipulation detection algorithms in realistic scenarios using real market and driver data from Spain. Our empirical results show that the decentralised algorithm's convergence to the optimal solution can be effectively disrupted by manipulative attacks achieving convergence to a different non-optimal solution which benefits the attacker. With respect to the detection algorithm, results indicate that it achieves very high accuracies and significantly outperforms a naive benchmark

Distributed control design for underwater vehicles

The vast majority of control applications are based on non-interacting decentralized control designs. Because of their single-loop structure, these controllers cannot suppress interactions of the system. It would be useful to tackle the undesirable effects of the interactions at the design stage. A novel model predictive control scheme based on Nash optimality is presented to achieve this goal. In this algorithm, the control problem is decomposed into that of several small-coupled mixed integer optimisation problems. The relevant computational convergence, closed-loop performance and the effect of communication failures on the closed-loop behaviour are analysed. Simulation results are presented to illustrate the effectiveness and practicality of the proposed control algorithm